I fixed it! Here's how:
I downloaded the latest AMD drivers for Windows 10 and installed them.
Then I downloaded the HP provided drivers for Windows 7
These drivers said that everything was up to date so I uninstalled the 5000 series in Device Manager, then rebooted.
After the reboot, I had Video Controller (VGA Compatible), I clicked on it and went to update drivers and choose to browse my computer.
I chose "C:\SwSetup\SP49517" and that installed the display drivers and the screen went black.
I waited a while to be sure that the drivers were installed and then turned off the laptop with the power button.
When the laptop powered back on, it was working.
Now both 5000 series and 4200 series are working.
The only problem is that Windows Update is trying to update the drivers so I'm scared to let it update, how do I stop it from updating the AMD drivers but allow it to download Windows updates?
I don't really care, as long as the 5470 works and it does, the games run like they ran before and YouTube videos work like they worked before.